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156 lines
6.5 KiB
HTML
156 lines
6.5 KiB
HTML
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<!-- #BeginEditable "doctitle" -->
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<title>Finding Graphs of Functions in Nature</title>
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<meta name="description" content="Activity to go and find functions in nature, and photograph them!" />
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<script>Author = 'Dyke, Jeremiah';</script>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Finding Graphs of Functions in Nature</h1>
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<p class="large">Go find functions in nature, and photograph them!</p>
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<p>Studying <a href="../sets/functions-common.html">Graphs of Functions</a>?</p>
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<p>Well, some graphs of functions appear a lot, so knowing their shapes gives you a much better shot at graphing them correctly and catching common errors.</p>
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<h2>What do you need?</h2>
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<ul>
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<li>Either a graphing calculator, or a printout of the <a href="../sets/functions-common.html">graphs of functions</a></li>
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<li>A park or nature trail with plenty of trees or backyard</li>
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<li>A camera</li>
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<li>A keen eye for natural (not human made) shapes</li>
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</ul>
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<p>Here are a few examples:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<td align="center">
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<p class="center"> </p>
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<p><img src="../algebra/images/y-mxpb-graph.svg" alt="y=mx+b graph" /></p>
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<p><span class="larger">f(x) = mx + b</span></p>
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</td>
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<td align="center">
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<p class="center"><img src="../sets/images/function-reciprocal.svg" alt="Reciprocal function" /></p>
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<p class="center"><span class="larger">f(x) = 1/x</span></p>
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</td>
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</tr>
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<tr>
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<td align="center">
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<p class="center"><img src="../sets/images/function-square.svg" alt="Square function" /></p>
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<p class="center"><span class="larger"> f(x) = x<sup>2</sup></span></p>
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</td>
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<td align="center">
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<p class="center"><img src="../sets/images/function-square-root.gif" alt="Square root function" width="308" height="160" /></p>
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<p class="center"><span class="larger">f(x) = √x</span></p>
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</td>
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</tr>
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<tr>
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<td align="center">
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<p class="center"><img src="../sets/images/function-absolute.svg" alt="Absolute Value function" /></p>
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<p class="center"><span class="larger">f(x) = |x|</span></p>
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</td>
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<td align="center"><img src="../sets/images/function-exponential-e.gif" alt="natural exponential function" width="344" height="199" />
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<br> <span class="larger">f(x) = e<sup>x</sup></span></td>
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</tr>
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</table>
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</div>
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<p>And here are some example photos we took to give you an idea:
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<br></p>
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<h2>Graph of f(x) = mx + b</h2>
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<p>The graph of f(x) = mx+b is a straight line, thus you are looking for something in nature that resembles a straight line. For example:</p>
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<p class="center"><img src="images/graphs-functions-nature-1.jpg" width="191" height="329" alt="stick straight line" />
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<br> TAKE A PIC!</p>
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<h2><br>
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Graph of f(x) = x<sup>2</sup> or -x<sup>2</sup></h2>
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<p>The graph of f(x) = x<sup>2</sup> looks like a U, and -x<sup>2</sup> is like a ∩, thus you are looking for something that resembles a U or ∩. For example:</p>
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<p class="center"><img src="images/graphs-functions-nature-2.jpg" width="159" height="183" alt="stick x squared" />
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<br> TAKE A PIC!</p>
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<h2><br>
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Graph of Square Root: f(x) = √x <br></h2>
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<p>The graph of f(x) = √x looks something like the lower case letter r, for example:</p>
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<p class="center"><img src="images/graphs-functions-nature-3.jpg" width="194" height="315" alt="stick square root" />
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<br> TAKE A PIC!</p>
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<h2><br>
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Graph of Absolute Value: f(x) = |x|<br></h2>
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<p>The graph of f(x) = |x| looks some thing like the letter V, for example:</p>
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<p class="center"><img src="images/graphs-functions-nature-4.jpg" width="196" height="311" alt="stick absolute function" />
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<br> TAKE A PIC!</p>
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<p><br> See what other graphs you can find...</p>
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<p><br> When done, compare your pics of nature to the graphs of functions and put together a presentation.</p>
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<p> </p>
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<p align="right">Activity courtesy of <a href="hands-on-math.html">Hands On Math</a></p>
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<div class="related">
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<a href="../sets/functions-common.html">Common Functions</a>
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<a href="index.html">Activity Index</a>
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Copyright © 2020 MathsIsFun.com
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